2001/12/31 by Lucio Fassarella, Bert Schroer
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th
paper · pdf · doi:10.1088/0305-4470/35/43/311
published as J.Phys.A35:9123-9164,2002 · 43 pages, references added, last section expanded, minor corrections and modifications in main text
arxiv created 2002/01/10 · openalex publication_date 2002/10/16 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Wigner's theory of positive energy representations of the Poincaré group has often been used to give additional justifications for the Lagrangian quantization approach to QFT. Here we show that by extension with a modular localization structure it can directly lead to the net of local algebras without the use of any point-like field coordinatization. The same modular methods reveal that among the irreducible representations there are two exotic types ( d = 1 + 2 massive anyons and d = 1 + 3 zero mass helicity towers) whose localization is string-like; in fact, their conversion into operator algebras leads to free string field theory. We also report on two attempts to extend the underlying spirit of the intrinsic (nonquantization) Wigner approach to the realm of interacting theories. Both aim at unravelling the structure of (Rindler) wedge-localized algebras and show, for the first time, the constructive power of the algebraic approach which, although conceived by Rudolph Haag more than 40 years ago, has primarily contributed to the structural understanding of QFT.